Title:Time-Frequency Analysis and the Dark Side of Representation Theory
Abstract:The group of operators on
 generated by a single translation  and a single modulation  is a familiar object of study in signal analysis. It forms a unitary representation of the so-called discrete Heisenberg group. As such, its analysis yields easily to classical methods when  is rational. But when is irrational, it provides instructive concrete examples of several pathological representation-theoretic phenomena. We shall introduce the relevant concepts from representation theory, discuss the rational case briefly, and then explore the irrational case in more detail. |